Geometric properties of images of cartesian products of regular Cantor sets by differentiable real maps

TL;DR

This paper establishes formulas for the dimensions of images of Cartesian products of regular Cantor sets under differentiable maps, extending understanding of their geometric properties.

Contribution

It provides new dimension formulas for images of Cartesian products of regular Cantor sets under differentiable maps, generalizing previous results.

Findings

Dimension formulas for arithmetic sums of regular Cantor sets

Dimension calculations for images of Cartesian products of Cantor sets

Extension of geometric properties to differentiable maps

Abstract

We prove dimension formulas for arihmetic sums of regular Cantor sets, and, more generally, for images of cartesian products of regular Cantor sets by differentiable real maps.